When 36 is subtracted from the square of a number the result is five times the number what is the positive solution?

Let the number be ( x ). The equation can be set up as ( x^2 - 36 = 5x ). Rearranging gives ( x^2 - 5x - 36 = 0 ). Using the quadratic formula, ( x = \frac{5 \pm \sqrt{(5)^2 - 4(1)(-36)}}{2(1)} = \frac{5 \pm \sqrt{169}}{2} = \frac{5 \pm 13}{2} ). This yields the solutions ( x = 9 ) and ( x = -4 ), so the positive solution is ( x = 9 ).